Semi-empirical mass flow model and calibration method for undeveloped flow regions in an air seeder

ABSTRACT

A method of determining a mass flow rate of product being applied with an agricultural implement includes the steps of:
         calibrating a pressure drop across a known distance in an air line at a number of air flow rates;   metering a product at a desired application rate into the air line at a selected air flow rate;   establishing a pressure drop across the known distance at the selected air flow rate, while the product is being metered;   calculating a specific pressure drop by dividing the established pressure drop by the determined pressure drop;   ascertaining the values of parameters A and B using the mathematical expression:
 
α=1+ Aμ+B √{square root over (μ)}
    where:
           α=specific pressure drop;   μ=mass loading ratio; and   A and B=parameters based on measured data for the specific product being applied; and   
           estimating a mass flow rate of the product being applied.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a non-provisional application based upon U.S. provisional patentapplication Ser. No. 62/092,525, entitled “SEMI-EMPIRICAL MASS FLOWMODEL AND CALIBRATION METHOD FOR UNDEVELOPED FLOW REGIONS IN AN AIRSEEDER”, filed Dec. 16, 2014, which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a system and method for measuringproduct flow in an agricultural implement, and, more particularly, tosuch a system and method used with an agricultural seeding implement.

2. Description of the Related Art

Generally, seeding implements are towed behind a tractor or other workvehicle via a hitch assembly secured to a rigid frame of a planter orseeder. These seeding implements typically include one or more groundengaging tools or openers that form a seed trench for seed depositioninto the soil. The openers are used to break the soil to enable seeddeposition. After the seeds are deposited, each opener is followed by apacker wheel that packs the soil on top of the deposited seeds.

Air seeders are commonly towed by a traction unit, e.g., an agriculturaltractor, to apply a material such as seed, fertilizer and/or herbicideto a field. An air seeder has as a primary component a wheeled air cartwhich includes one or more frame-mounted tanks for holding material. Inthe case of multiple tanks, the tanks can be separate tanks, or a singletank with internal compartments. The air cart is typically towed incombination with a tilling implement, such as an air drill, one behindthe other, to place the seed and fertilizer under the surface of thesoil. Air seeders generally include a metering system for dispensingmaterial from the tanks and a pneumatic distribution system fordelivering the material from the tanks to the soil. A centrifugal fanprovides at least one airstream which flows through the pneumaticdistribution system. Material is first introduced to the air stream bythe metering system at a primary distribution manifold located below themetering system. The tanks of the air seeders are formed with bottomsurfaces that slope downward at an angle of repose for the granularmaterial toward the metering system. Gravity, in combination with thevibrations and movement of the air seeder, act to move the granularmaterial from the perimeter of the tank toward the metering systemlocated at the center of the tank. Material is carried by the air streamthrough distribution lines to a series of secondary distributionmanifolds, which in turn distribute the material through distributionlines to seed boots mounted behind ground openers on the tillingimplement so that the product may be evenly delivered to the groundwhich is tilled by the tilling implement.

To ensure that a desired quantity of product is delivered, a calibrationprocedure may be performed to calibrate rotation of meter rollers withinthe metering system to a mass flow rate of product to the openers. Somecalibration procedures involve user intervention throughout the process.For example, a user may attach a bag to the metering system to collectexpelled product. The user may then instruct the metering system torotate the meter rollers through a desired number of rotations (e.g., 50100, 150, 200, etc.). Next, the user may weigh the collected product andenter the weight into a user interface. A controller may thenautomatically compute a calibration that associates product mass flowrate with rotation of the meter rollers. Such user intervention may betime consuming, and may result in inaccurate calibrations, therebycausing too much or too little product to be delivered.

Current product delivery systems assume that the meter roller has beenproperly calibrated and remains operating properly throughout usage. Airseeders currently do not provide feedback on the product mass flow rateof the product being conveyed. With a technology shift towardvariable-rate and independent control of product flow rates, knowledgeof the actual flow within the air seeder will be important to properlycontrolling the air delivery system. Existing methods for pressure-basedmass flow rate determination are either purely empirical, or rely on theflow being fully accelerated and the air velocity being well above aminimum conveying velocity of the product being conveyed. Neither ofthese conditions are amenable to application on an air cart/drill.

For example, U.S. Pat. No. 8,746,158 (which is assigned to the assigneeof the present invention) discloses a pressure based mass flow ratesystem and method using empirical data. A controller receives pressuresensor signals to determine a pressure drop across a known length ofpipe, and compares the pressure drop with data from an empiricalpressure database.

What is needed in the art is a faster and more accurate system andmethod for determining the mass flow rate of a product being conveyed inan air seeder, particularly in regions of undeveloped air flow withinthe product delivery system.

SUMMARY OF THE INVENTION

The present invention provides a product measurement system for use inan air seeder which provides feedback concerning the actual mass flowrate of the product being applied, and is easier to calibrate on siteduring use.

The invention in one form is directed to a method of determining a massflow rate of product being applied with an agricultural implement,including the steps of:

providing an air flow from a pressure source at a known air flow rate inan air line;

determining a pressure drop in the air line along a known distance in adownstream direction using at least one pressure sensor, each pressuresensor being positioned downstream from the pressure source;

repeating the providing and determining steps at a plurality of knownair flow rates;

metering a product at a desired application rate into the air line at aselected one of the air flow rates;

establishing a pressure drop across the known distance at the selectedair flow rate, while the product is being metered at the desiredapplication rate;

calculating a specific pressure drop by dividing the establishedpressure drop by the determined pressure drop, at the selected air flowrate;

ascertaining the values of parameters A and B using the mathematicalexpression:α=1+Aμ+B√{square root over (μ)}

-   -   where:    -   α=specific pressure drop;    -   μ=mass loading ratio; and    -   A and B=parameters based on measured data for the specific        product being applied; and

estimating a mass flow rate of the product being applied.

The invention in another form is directed to a mass flow measurementsystem for determining a mass flow rate of product being applied with anagricultural implement. The mass flow measurement system includes:

a pressure source in communication with an air line;

an air flow sensor in communication with the air line, the air flowsensor being positioned downstream from the pressure source;

a metering device in communication with the air line, the meteringdevice being positioned downstream from the air flow sensor;

at least one pressure sensor in communication with the air line, eachpressure sensor being positioned downstream from the metering device;

a controller coupled with each of the pressure source, the air flowsensor, the metering device, and the at least one pressure sensor, thecontroller being configured for:

-   -   actuating the pressure source to provide an air flow at a known        air flow rate in the air line using the air flow sensor;    -   determining a pressure drop in the air line along a known        distance in a downstream direction using the at least one        pressure sensor;    -   repeating the actuating and determining steps at a plurality of        known air flow rates;    -   metering a product at a desired application rate into the air        line at a selected one of the air flow rates using the metering        device;    -   establishing a pressure drop across the known distance at the        selected air flow rate using the at least one sensor, while the        product is being metered at the desired application rate;    -   calculating a specific pressure drop by dividing the established        pressure drop by the determined pressure drop, at the selected        air flow rate;    -   ascertaining the values of parameters A and B using the        mathematical expression:        α=1+Aμ+B√{square root over (μ)}    -    where:        -   α=specific pressure drop;        -   μ=mass loading ratio; and        -   A and B=parameters based on measured data for the specific            product being applied; and    -   estimating a mass flow rate of the product being applied.

An advantage of the present invention is that the mass flow rate can beestimated in areas of undeveloped air flow, without requiring long,straight runs.

Another advantage is that the system should be easier to calibrate,having fewer cooefficients to solve for and simpler mathematicalrelationships. Thus, fewer data points are needed to calibrate.

Yet another advantage is that the one or more sensors can be factorycalibrated, and only need a validation/correction in the field.

Yet a further advantage is that it is feasible to develop correlationsfor the model coefficients based on particle characteristics, furthersimplifying the calibration process.

BRIEF DESCRIPTION OF THE DRAWINGS

The above-mentioned and other features and advantages of this invention,and the manner of attaining them, will become more apparent and theinvention will be better understood by reference to the followingdescription of an embodiment of the invention taken in conjunction withthe accompanying drawings, wherein:

FIG. 1 is a partial, side schematic illustration of an embodiment of anair seeder which can be used with the system and method of the presentinvention;

FIG. 2 is a schematic illustration of an embodiment of a product flowmeasurement system of the present invention; and

FIG. 3 is a flow chart illustrating an embodiment of a method ofdetermining a mass flow rate of product being applied in an agriculturalair seeder.

Corresponding reference characters indicate corresponding partsthroughout the several views. The exemplification set out hereinillustrates an embodiment of the invention, and such exemplification isnot to be construed as limiting the scope of the invention in anymanner.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings, and more particularly to FIG. 1, there isshown a partial, side schematic illustration of an embodiment of anagricultural implement in the form of an air seeder 10 of the presentinvention. Air seeder 10 generally includes an air cart 12 which istowed by a tilling implement 14 (with only a portion of the rear hitch16 of tilling implement 14 showing in FIG. 1). In the embodiment shown,tilling implement 14 is in the form of an air drill, but can bedifferently configured, depending upon the application. For example,tilling implement 14 could be in the form of a planter and air cart 12could be used to refill mini-hoppers onboard the planter. Air cart 12may also be configured with a rear hitch (not shown) allowing air cart12 to be towed in front of, rather than behind, tilling implement 14.

Air cart 12 generally includes a frame 18 which carries steerable frontwheels 20, rear wheels 22, tank 24, an air source in the form of ablower 26, and an auger 28. Tank 24 is illustrated as amulti-compartment tank with internal divider walls (not shown)separating the compartments. In the embodiment shown, tank 24 has threecompartments 24A, 24B and 24C with each compartment containing amaterial to be deposited into the soil (such as seed, fertilizer,herbicide and/or insecticide). Each compartment 24A, 24B and 24C has atop hatch 30 allowing loading of the material therein.

Air cart 12 includes a product delivery system in the form of apneumatic distribution system 32 for delivering the air-entrainedmaterial to the trenches in the soil formed by tilling implement 14.Pneumatic distribution system 32 includes a metering system 34 (notspecifically shown in FIG. 1, but illustrated in FIG. 2 discussedbelow), blower 26 and a plurality of air lines 36. Air lines 36 extendforward to and terminate at a convenient location for coupling with airlines 38 associated with tilling implement 14.

In the illustrated embodiment, blower 26 is a centrifugal blower, butcan be differently configured. Further, in the illustrated embodiment,three primary air lines 36 are shown, one from each tank compartment24A, 24B and 24C. However, the number of air lines 36 can vary,depending on the application.

Referring now to FIG. 2, the air seeder 10 shown in FIG. 1 may include aproduct flow measurement system 40 for measuring product flow deliveredto the trenches formed in the soil. In the illustrated embodiment, theproduct flow measurement system 40 includes an air source in the form ofblower 26 which is configured to provide an air flow 42 into the airlines 36. The metering device 34 is configured to deliver product intothe air flow 42, thereby establishing a product/air mixture that flowsin a downstream direction toward the implement 14. In the illustratedembodiment, the product flow measurement system 40 is configured todetermine a mass flow rate of product through the air lines 36. Asillustrated, the product flow measurement system 40 may include a firstpressure sensor 44 configured to measure fluid pressure within anupstream portion of the air line 36, and a second pressure sensor 46spaced from first pressure sensor 44 at a known distance and configuredto measure fluid pressure within a downstream portion of the air line36. The first pressure sensor 44 is fluidly coupled to the air line 36via a first pressure tap 48, and the second pressure sensor 46 isfluidly coupled to the air line 36 via a second pressure tap 50. Thesensors 44 and 46 are configured to measure the fluid pressure withinthe conduit 38 via the respective pressure taps 48 and 50, and to outputrespective signals indicative of the measured pressure. As will beappreciated, the first and sensor pressure sensors may include fiberoptic sensors, mechanical deflection sensors, piezoelectric sensors,microelectromechanical system (MEMS) sensors, or any other suitablesensor configured to output a signal indicative of fluid pressure withinthe air line 36.

The product flow measurement system 40 also includes an air flow sensor52 positioned upstream from the metering device 34. The air flow sensor52 is configured to measure a flow rate of the air flow 42, and avelocity of the air flow 42. In certain embodiments, the air flow sensor52 can include an orifice plate having an aperture with a smallerdiameter than the air line 36. As the air flow 42 passes through theaperture, the fluid pressure decreases and the velocity increases. Bymeasuring the pressure difference between the air flow upstream anddownstream of the aperture, the flow rate (e.g., volumetric flow rate,mass flow rate, etc.) of air flow 42 may be determined. In otherembodiments, the air flow sensor 52 can include a hot wire sensor havingan electrically heated element extending through the air flow. As willbe appreciated, heat transfer from the wire to the air flow is at leastpartially dependent on the flow rate of the air flow across the wire.Therefore, by measuring the electrical current sufficient to heat thewire to a desired temperature, the flow rate of air flow 42 may bedetermined. It should also be appreciated that alternative embodimentsmay include other suitable air flow sensors configured to measure flowrate and/or velocity of the air flow 40. As will be appreciated, if avolumetric flow rate is measured, the mass flow rate may be calculatedbased on the density of the air.

In the illustrated embodiment, the first pressure sensor 44, the secondpressure sensor 46 and the air flow sensor 52 are communicativelycoupled to a controller 54. The controller 54 can be variouslyconfigured, such as a digital controller, analog controller, or acombination of the two, etc. The controller 54 is configured to receivea first signal from the first pressure sensor 44 indicative of fluidpressure within the upstream portion of the air line 36, and to receivea second signal from the second pressure sensor 46 indicative of fluidpressure within the downstream portion of the air line 36. Thecontroller 54 is also configured to receive a third signal from the airflow sensor 52 indicative of a flow rate of air flow 42, and may receivea fourth signal from the air flow sensor 52 indicative of a velocity ofthe air flow. Alternatively, the controller 54 may be configured toreceive the third signal or the fourth signal, and to determine both themass flow rate of the air flow and/or the velocity of the air flow basedon the single signal. Once the signals have been received, thecontroller 54 may determine a pressure drop between the upstream anddownstream portions of the air line 36 based on the first and secondsignals. The controller 54 may then determine a mass flow rate ofproduct through the fluid conduit based on the pressure drop, the massflow rate of the air flow and the velocity of the air flow.

While the illustrated embodiment includes separate pressure sensors 44and 46, it should be appreciated that alternative embodiments mayinclude a single pressure sensor configured to directly measure thepressure drop between the upstream and downstream portions of the airline 36. For example, in certain embodiments, a differential pressuresensor may be fluidly coupled to the first pressure tap 48, and to thesecond pressure tap 50. In such embodiments, the differential pressuresensor may be configured to output a signal indicative of the pressuredifference (i.e., pressure drop) between the upstream portion of the airline 36 and the downstream portion of the air line 36. Accordingly, thecontroller 54 may determine the product mass flow rate based on thedifferential pressure signal.

For precision farming applications, a spatial locating device 56 (e.g.,GPS unit) can be used to provide spatial data to the controller 54indicative of a geo-spatial location of the air seeder within a field.The spatial data can be matched with data from soil charts, applicationrates, etc. for the field to carry out variable application seeding withthe air seeder 10.

A user interface 58 allows an operator to enter various input data intothe controller 54 for operation of the air seeder 10. For example, theuser could enter a particular type of material to be applied, whetherthe operator wishes to use constant or variable rate application, etc.The user interface can be any suitable type of interface, such as atouch screen, keyboard, etc.

As indicated above, known models for determining a mass flow rate of theproduct being dispensed assume that the metering device works properlyafter being calibrated, and also assume that the product is fullysuspended in the air stream, each of which may be faulty assumptions.There is no way to know if the product mass flow rate changes outside ofacceptable limits. Further, known models may also calculate for thepressure drop factor for solids (λ_(Z)) in a simplified form byneglecting the effect of gravity. That assumption can be made when theparticles have travelled far enough to be considered fully suspended.But when the pressure drop measurement comes within the first meter orso, neglecting gravitational effect may not be a valid assumption,especially, for lower superficial air velocities.

According to an aspect of the present invention, feedback is provided tothe controller 54 to determine if the dispense rate of the meteringdevice falls outside of acceptable limits, and the effects of gravity innon-developed areas of flow are included in the model. To that end, acomplete representation of the pressure drop factor for solids (λ_(Z)),including the effects of gravity in areas of flow which are not fullydeveloped, is shown in Equation [1],

$\begin{matrix}{{\lambda_{Z} = {{\lambda_{Z}^{*}\frac{c}{v}} + \frac{2\beta}{\frac{c}{v}{Fr}^{2}}}},} & \lbrack 1\rbrack\end{matrix}$

where λ_(Z)* is the impact and friction factor for solids[dimensionless],

-   -   c is the particle velocity [m/s],    -   v is the superficial air velocity [m/s],    -   β is the velocity ratio related to particle fall velocity in a        cloud [dimensionless], and    -   Fr is the Froude number [dimensionless].

The Froude number (Fr) in Equation [1] is the ratio of inertial forceand gravitational force, whereas β is the ratio of particle fallvelocity due to gravity and superficial air velocity. With therepresentation of pressure drop according to Equation [1], theexpression for specific pressure drop takes the form:

$\begin{matrix}{\alpha = {1 + {( \frac{{\lambda_{Z}^{*}\frac{c}{v}} + \frac{2\beta}{\frac{c}{v}{Fr}^{2}}}{\lambda_{L}} ){\mu.}}}} & \lbrack 2\rbrack\end{matrix}$

In separate experiments, the relationship between mass loading ratio (μ)and Froude number (Fr) at the pressure minimum condition have beendetermined. Experiments have been conducted with Polystyrol (diameter 1mm-2.5 mm) inside carbon steel pipe. The developed relationship wasvalid for pipe diameters of 50 mm-400 mm. It is given byμ=KFr ⁴,  [3]where K is an experimental constant [dimensionless].

Assuming Equation [3] is valid for this disclosure as well, putting

${Fr}^{2} = \sqrt{\frac{\mu}{K}}$in equation [2] gives the expression for specific pressure drop as

$\begin{matrix}{\alpha = {1 + {( \frac{\lambda_{Z}^{*}}{\lambda_{L}} )( \frac{c}{v} )\mu} + {\frac{2\beta\sqrt{K}}{( \frac{c}{v} )\lambda_{L}}{\sqrt{\mu}.}}}} & \lbrack 4\rbrack \\{{{{Letting}\mspace{14mu} A} = {( \frac{\lambda_{Z}^{*}}{\lambda_{L}} )( \frac{c}{v} )}},} & \lbrack 5\rbrack \\{{{{and}\mspace{14mu} B} = \frac{2\beta\sqrt{K}}{( \frac{c}{v} )\lambda_{L}}},} & \lbrack 6\rbrack\end{matrix}$equation [4] then takes the form:α=1+Aμ+B√{square root over (μ)}.  [7]

Equation [7] has both linear and non-linear components. If the value ofB is substantially smaller compared to the value of A, the specificpressure drop vs. mass loading ratio should be linear. If gravitationaleffects become significant at lower velocities, the plot will becomenon-linear because the value of B in that case will not be negligible.The experimental plots obtained when pressure drop was measured inbetween 0.3 m and 0.9 m of the test section, were also linear for highervelocities and nonlinear for lower velocities. To see whether Equation[7] can represent both the linear and nonlinear trends observed in theexperiments, it was optimized to determine the values of unknownparameters A and B at each air velocity being considered.

Optimization of the parameters A and B was carried out by using theMATLAB engineering analysis software and an appropriate algorithm. Theselected algorithm is best suited for non-linear optimization. Table 1lists the value of parameters A and B for different air velocities, anda selected product type (the values of A and B vary, depending onproduct/particle type (e.g., wheat, corn, granular herbicide, granularfertilizer, etc)).

TABLE 1 Values of parameters A and B at different air velocities AirVelocity (m/s) Value of A Value of B 30 1.7818 −0.1287 28 1.6573 0.178426 1.6494 0.2547 24 1.387 0.4825 22 1.0593 0.7139 20 0.5058 1.1983 180.2056 1.5464 16 −0.2585 2.0845 14 −0.4723 2.2856 13 −0.1951 1.965

It can be seen from the table that the value of A dominates at highervelocities. As the air velocity decreases, the value of B starts todominate. All of these optimizations had an R-Square value greater than0.99. Equations [5] and [6] suggest that parameters A and B are ratiosof positive dimensionless numbers and velocity magnitudes. Hence theycannot have negative values. For this reason optimized values of A and Bwere adjusted with the curve fitting tool of the MATLAB software. Theadjusted values of A and B (with 95% confidence interval) are presentedin Table 2 along with the R-Square values.

TABLE 2 Adjusted values of Parameter A and B at different air velocitiesAir Velocity (m/s) Value of A Value of B R-Square 30 1.65 0.05 0.9923 291.65 0.15 0.9977 28 1.65 0.20 0.9977 27 1.65 0.25 0.9850 26 1.65 0.300.9953 25 1.48 0.40 0.9966 24 1.39 0.48 0.9962 23 1.25 0.53 0.9951 221.06 0.71 0.9969 21 0.95 0.79 0.9919 20 0.75 0.93 0.9842 19 0.65 1.030.9857 18 0.48 1.23 0.9840 17 0.23 1.37 0.9804 16 0.15 1.61 0.9747 150.001 1.72 0.9703

The value of parameter A remains constant at higher velocities andgradually decreases with air velocity. This indicates that even whenpressure drop is measured closer to the metering device 34, the majorityof the particles are fully accelerated at higher velocities. For thisreason the value of A remains substantially constant. But due to thepresence of parameter B (i.e., due to some particles not attaining fullacceleration), the overall value of the slope was different at highervelocities. Below 15 m/s the value of A becomes negative. Therefore,based on the MATLAB analysis, the model presented in Equation [7] isvalid for air velocities from 15 m/s-30 m/s.

The product mass flow analysis model described above accounts forparticle interaction and acceleration effects that apply at lowconveying velocities and the undeveloped region. These factors introducenon-linarites into the specific pressure drop (α=pressure drop for airand product/pressure drop for air only), vs mass loading ratio μrelationship. In one embodiment, and referring to FIG. 3, the mass flowrate of the product in the air seeder 10 for use with the modeldescribed above can be accomplished using the following method:

Step 1: System records pressure drop over the entire range of velocityfor air only once operator starts machine (block 70).

Step 2: Operator dispenses product at desired roller speed and airvelocity and system records pressure drop (block 72 and 74).

Step 3: Calculate specific pressure at the operating velocity (bydividing pressure drop due to the mixture by pressure drop due to aironly (block 76).

Step 4: Determine the value of parameters A and B (block 78).

Step 5: Estimate mass flow rate of the product being applied (block 80).In a similar manner, the mass flow rate of any product can be estimated.The basic form of the model will remain the same as Equation [7], whichis given by α=1+Aμ+B(μ)^½. This relationship must be developed betweenparameters A and B, and the average air velocity separately for eachproduct.

In the example above, Steps 2, 3 and 4 establish the parameters A and Bbased on measured data for the specific product being applied. However,it may also be possible to use empirical data for the product beingapplied to determine the values of the parameters A and B. For example,the controller 54 may be configured to establish a relationship betweenthe measured parameters (i.e., flow rate of the air flow, velocity ofthe air flow, and pressure drop through the air line) and the mass flowrate of product through the air line based on empirically derivedparameters. For example, at least one empirical parameter may beassociated with each product (e.g., seed, fertilizer, etc.), and thecontroller 54 may be configured to determine the mass flow rate ofproduct through the air line 36 based on the pressure drop, the massflow rate of the air flow, the velocity of the air flow, and theempirical parameters. The empirical parameters may be stored in anon-volatile memory 60, which includes a list of products and acorresponding list of empirical parameters. By way of example, prior tooperation of the air seeder 10, an operator may select the type ofproduct (e.g., seed, fertilizer, etc.) stored within the tank 24 of theair cart 12 via a user interface 58. The controller 54, in turn, mayselect the appropriate empirical parameters from the memory 60 based onthe selected product. During operation of the air seeder 10, thecontroller 54 may determine the mass flow rate of product to theimplement 14 based on the pressure drop, the flow rate of the air flow,the velocity of the air flow, and the empirical parameters associatedwith the product flowing to the ground engaging tools of the implement14.

While this invention has been described with respect to at least oneembodiment, the present invention can be further modified within thespirit and scope of this disclosure. This application is thereforeintended to cover any variations, uses, or adaptations of the inventionusing its general principles. Further, this application is intended tocover such departures from the present disclosure as come within knownor customary practice in the art to which this invention pertains andwhich fall within the limits of the appended claims.

What is claimed is:
 1. A method of determining a mass flow rate ofproduct being applied with an agricultural implement, comprising thesteps of: providing an air flow from a pressure source at a known airflow rate in an air line; determining a pressure drop in the air linealong a known distance in a downstream direction using at least onepressure sensor, each said pressure sensor being positioned downstreamfrom the pressure source; repeating the providing and determining stepsat a plurality of known air flow rates; metering a product at a desiredapplication rate into the air line at a selected one of the air flowrates; establishing a pressure drop across the known distance at theselected air flow rate, while the product is being metered at thedesired application rate; calculating a specific pressure drop bydividing the established pressure drop by the determined pressure drop,at the selected air flow rate; ascertaining the values of parameters Aand B using the mathematical expression:α=1+Aμ+B√{square root over (μ)}  where: α=specific pressure drop; μ=massloading ratio; and A and B=parameters based on measured data for thespecific product being applied; and estimating a mass flow rate of theproduct being applied.
 2. The method of claim 1, wherein the parameter Ais represented by the mathematical expression:$A = {( \frac{\lambda_{Z}^{*}}{\lambda_{L}} )( \frac{c}{v} )}$and the parameter B is represented by the mathematical expression:${B = \frac{2\beta\sqrt{K}}{( \frac{c}{v} )\lambda_{L}}},$where: λ_(Z)=impact and friction factor for solids; λ_(L)=air resistancecoefficient; c=particle velocity of the product in the air flow;v=average/superficial air velocity; β=velocity ratio related to particlefall velocity in a cloud; and K=dimensionless experimental constant. 3.The method of claim 1, wherein the mass loading ratio μ is defined bythe mathematical expression:μ=KFr ⁴, where: Fr=Froude number (Fr) at a pressure minimum condition;and K=dimensionless experimental constant.
 4. The method of claim 1,wherein the parameters A and B are determined based upon emperical datacorresponding to a specific product being applied.
 5. The method ofclaim 4, wherein the parameters A and B are determined based uponemperical data which is stored in a memory.
 6. The method of claim 4,wherein the selected product includes seed, fertilizer, herbicide orinsecticide.
 7. The method of claim 1, wherein the at least one sensorincludes a first pressure sensor and a second pressure sensor which arespaced apart at the known distance, and the determining step includesdetermining a pressure drop in the air line between the first pressuresensor and the second pressure sensor, the first pressure sensor beingdownstream from the pressure source and the second pressure sensor beingdownstream from the first pressure sensor.
 8. The method of claim 1,wherein the providing step is carried out using an air flow sensor inthe air line to determine the known air flow rate.
 9. The method ofclaim 1, wherein the air flow sensor is positioned between the pressuresource and the at least one pressure sensor.
 10. The method of claim 1,wherein the known air flow rate includes at least one of a volumetricflow rate and a velocity of the air flow.
 11. The method of claim 1,wherein the agricultural implement is an air seeder.
 12. A mass flowmeasurement system for determining a mass flow rate of product beingapplied with an agricultural implement, said mass flow measurementsystem comprising: a pressure source in communication with an air line;an air flow sensor in communication with the air line, said air flowsensor being positioned downstream from the pressure source; a meteringdevice in communication with the air line, said metering device beingpositioned downstream from the air flow sensor; at least one pressuresensor in communication with the air line, each said pressure sensorbeing positioned downstream from the metering device; a controllercoupled with each of the pressure source, the air flow sensor, themetering device, and the at least one pressure sensor, the controllerbeing configured for: actuating the pressure source to provide an airflow at a known air flow rate in the air line using the air flow sensor;determining a pressure drop in the air line along a known distance in adownstream direction using the at least one pressure sensor; repeatingthe actuating and determining steps at a plurality of known air flowrates; metering a product at a desired application rate into the airline at a selected one of the air flow rates using the metering device;establishing a pressure drop across the known distance at the selectedair flow rate using the at least one sensor, while the product is beingmetered at the desired application rate; calculating a specific pressuredrop by dividing the established pressure drop by the determinedpressure drop, at the selected air flow rate; ascertaining the values ofparameters A and B using the mathematical expression:α=1+Aμ+B√{square root over (μ)}  where: α=specific pressure drop; μ=massloading ratio; and A and B=parameters based on measured data for thespecific product being applied; and estimating a mass flow rate of theproduct being applied.
 13. The mass flow measurement system of claim 12,wherein the parameter A is represented by the mathematical expression:$A = {( \frac{\lambda_{Z}^{*}}{\lambda_{L}} )( \frac{c}{v} )}$and the parameter B is represented by the mathematical expression:${B = \frac{2\beta\sqrt{K}}{( \frac{c}{v} )\lambda_{L}}},$where: λ_(Z)=impact and friction factor for solids; λ_(L)=air resistancecoefficient; c=particle velocity of the product in the air flow;v=average/superficial air velocity; β=velocity ratio related to particlefall velocity in a cloud; and K=dimensionless experimental constant. 14.The mass flow measurement system of claim 12, wherein the mass loadingratio μ is defined by the mathematical expression:μ=KFr ⁴, where: Fr=Froude number (Fr) at a pressure minimum condition;and K=dimensionless experimental constant.
 15. The mass flow measurementsystem of claim 12, wherein the parameters A and B are determined basedupon emperical data corresponding to a specific product being applied.16. The mass flow measurement system of claim 15, wherein the parametersA and B are determined based upon emperical data which is stored in amemory.
 17. The mass flow measurement system of claim 15, wherein theselected product includes seed, fertilizer, herbicide or insecticide.18. The mass flow measurement system of claim 12, wherein the at leastone sensor includes a first pressure sensor and a second pressure sensorwhich are spaced apart at the known distance, and the determining stepincludes determining a pressure drop in the air line between the firstpressure sensor and the second pressure sensor, the first pressuresensor being downstream from the pressure source and the second pressuresensor being downstream from the first pressure sensor.
 19. The massflow measurement system of claim 12, wherein the known air flow rateincludes at least one of a volumetric flow rate and a velocity of theair flow.
 20. The mass flow measurement system of claim 12, wherein theagricultural implement is an air seeder.